On the Weight Hierarchy of Product Codes

Let V and W be codes and let C = V W be the product code of V and W. In [6] Wei and Yang, conjectured a formula for the generalized Hamming weights of V W in terms of those of V and W provided that both V and W satisfy the chain condition. Recently the conjecture has been proved by Schaathun [4]. In this paper we generalize the formula to a product code with more than two components.     

关于外积码的Hamming谱

本文研究了任意有限域Fq上的两个线性码的外积及其有关性质；并给出了由两个线性码构造的外积码的Hamming谱的第1个谱值的界以及最后一个谱值。     

Weight Hierarchies of Linear Codes Satisfying the Chain Condition

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d₁,d₂,...,d_k) where d_r is the smallest support of an r–dimensional subcode of C. By explicit construction, it is shown that if a sequence (a₁,a₂,...,a_k) satisfies certain conditions, then it is the weight hierarchy of a code satisfying the chain condition.     

Finite Projective Geometries and Classification of the Weight Hierarchies of Codes （Ⅰ）

The weight hierarchy of a binary linear [n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ).     

Maximal Weight Divisors of Projective Reed-Muller Codes

Projective Reed-Muller (PRM) codes, as the name suggests, are the projective analogues of generalized Reed-Muller codes. The parameters are known, and small steps have been taken towards pinning down the codeword weights that occur in any PRM code. We determine, for any PRM code, the greatest common divisor of its codeword weights.     

Improvements on Generalized Hamming Weights of Some Trace Codes

We obtain improved bounds for the generalized Hamming weights of some trace codes which include a large class of cyclic codes over any finite field. In particular, we improve the corresponding bounds of Stichtenoth and Voss [8] using various methods altogether.     

On the Minimum Length of some Linear Codes of Dimension 5

In this paper, we shall prove that the minimum length n_q(5,d) is equal to g_q(5,d) +1 for q⁴−2q²−2q+1≤ d≤ q⁴ − 2q² − q and 2q⁴ − 2q³ − q² − 2q+1 ≤ d ≤ 2q⁴−2q³−q²−q, where g_q(5,d) means the Griesmer bound . Communicated by: J.D. Key     

M-矩阵Hadamard积的最小特征值下界的新估计式

设B和A是非奇异M-矩阵,给出B和A-1的Hadamard积的最小特征值下界τ（B°A-1）的一个新估计式,理论证明和算例表明,本文所得新估计式改进了现有的一些结果．     

Minihypers and Linear Codes Meeting the Griesmer Bound: Improvements to Results of Hamada, Helleseth and Maekawa

This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any -minihyper, with , where , is the disjoint union of points, lines,..., -dimensional subspaces. For q large, we improve on this result by increasing the upper bound on non-square, to non-square, square, , and (4) for square, p prime, p<3, to . In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry . For the coding-theoretical problem, our results classify the corresponding codes meeting the Griesmer bound.     

求解社区项目博弈的一种改进贪婪算法研究

针对社区项目博弈的一般模型,应用贪婪算法求解项目博弈的近似社会最优指派,给出参与者重加权分配机制,证明贪婪算法求得的指派恰好是非合作项目博弈的一个纳什均衡.定义控制参数,给出边际效益后悔值定义,利用后悔值改进了贪婪算法,证明基于后悔值贪婪算法求得的指派是非合作项目博弈的一个纳什均衡.通过数值仿真实验发现,与模拟退火算法比较,贪婪算法能够得到更好的社会效益,而且基于后悔值贪婪算法比贪婪算法得到更好的社会效益.     

On the Minimum Weight of Codes over F5 Constructed from Certain Conference Matrices

In this paper, codes over F₅ with parameters [36, 18, 12], [48, 24, 15], [60, 30, 18], [64, 32, 18] and [76, 38, 21] which improve the previously known bounds on the minimum weight for linear codes over F₅ are constructed from conference matrices. Through shortening and truncating, the above codes give numerous new codes over F₅ which improve the previously known bounds on minimum weights.     

关于“一致有界的一族无穷小的积是无穷小”定理

针对微积分教材关于"无穷小的积是否是无穷小"的命题的模糊叙述,证明"一致有界的一族无穷小的积仍是无穷小".     

On the Influence of Weights on Extremes

Let X ₁, ..., X_n be an i.i.d. sequence of random variables, from an unknown distribution F, and X ₁ ^W , ... X _n ^W be a sample from , the weighted empirical distribution function of X ₁, ..., X_n. We define the order statistics X _1,n ^W ... X _n,n ^W of X ₁ ^W , ..., X _n ^W . Under suitable assumptions on weights, we study the influence of the maxima in the construction of limit theorems. We choose a resample size m(n) and we derive conditions on m(n) for the in probability and with probability 1 consistency of X _m(n),m(n) ^W . The presence of weights has an influence on the resample size and requires the use of new tools. When X _n,n is in the domain of attraction of an extreme value distribution, m(n) , and , as n , all our results hold.     

A Necessary and Sufficient Condition for the Existence of Some Ternary [n, k, d] Codes Meeting the Greismer Bound

Let k and d be any integers such that k 4 and . Then there exist two integers and in {0,1,2} such that . The purpose of this paper is to prove that (1) in the case k 5 and (,) = (0,1), there exists a ternary code meeting the Griesmer bound if and only if and (2) in the case k 4 and (,) = (0,2) or (1,1), there is no ternary code meeting the Griesmer bound for any integers k and d and (3) in the case k 5 and , there is no projective ternary code for any integers k and such that 1k-3, where and for any integer i 0. In the special case k=6, it follows from (1) that there is no ternary linear code with parameters [233,6,154] , [234,6,155] or [237,6,157] which are new results.     

A Lower Bound on the Growth of Word Hyperbolic Groups

We give a linear lower bound on the exponential growth rateof a non-elementary subgroup of a word hyperbolic group, withrespect to the number of generators for the subgroup.     

A Lower Bound Sequence for the Minimum Eigenvalue of Hadamard Product of an M-Matrix and its Inverse

Czechoslovak Mathematical Journal - We propose a lower bound sequence for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse, in terms of an S-type eigenvalues inclusion set...     

图的第四大无符号拉普拉斯特征值的一个下界

设G是一个阶数大于等于4的简单连通图．代4（G）和d4（G）分别表示G的第四大无符号拉普拉斯特征值和第四大度．本文证明了K4（G）≥d4（G）一2．